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 引用本文: 张耀明 刘召颜 李功胜 屈文镇. 各向异性位势平面问题的规则化边界元法[J]. 力学学报, 2011, 43(4): 785-789.
Zhang Yaoming Liu Zhaoyan Li Gongsheng Qu Wenzhen. A regularized boundary element method for anisotropic potential problems[J]. Chinese Journal of Theoretical and Applied Mechanics, 2011, 43(4): 785-789.
 Citation: Zhang Yaoming Liu Zhaoyan Li Gongsheng Qu Wenzhen. A regularized boundary element method for anisotropic potential problems[J]. Chinese Journal of Theoretical and Applied Mechanics, 2011, 43(4): 785-789.

## A regularized boundary element method for anisotropic potential problems

• 摘要: 基于转化域方程为边界积分方程的极限定理及一个新颖的基本解分解技术, 建立间接变量规则化边界积分方程, 它有效地避免了奇异积分的直接计算. 与已有方法比,该方法不将问题变换为各向同性的问题去处理, 因而无需反演运算, 也有别于Galerkin方法, 无需计算重积分. 可计算任意边界位势梯度, 而不仅限于法向通量. 针对椭圆边界的边值问题, 提交一种精确单元来描述边界几何. 数值算例表明, 所提算法稳定且效率高, 所得数值结果与精确解吻合较好.

Abstract: The presentation is mainly devoted to the research on theregularized BEM formulations for homogeneous anisotropic potential problems.Based on a limit theorem for the transformation from domain integralequations into boundary integral equations (BIEs) and a novel decompositiontechnique to the fundamental solutions, the regularized BIEs with indirectunknowns, which don't involve singular integrals, are established. Comparedwith the existing methods, the presented method can solve theconsidered problems directly instead of transforming them into isotropicones, and for this reason, no inverse transform is required. In addition,this method doesn't require to calculate multiple integral as the Galerkinmethod, but rather evaluate CPV integrals indirectly, and so it is simpleand easy to program. Furthermore, the proposed gradient BIEs are suited forthe computation of \partial u/\partial x_i (i =1,2) on the boundary, not only limited to normal flux \partial u/\partial n. Especially, for the boundary valueproblems with elliptic boundary, an exact element is developed to model itsboundary with almost no error. The convergence and accuracy of the proposedalgorithm are investigated and compared for several numerical examples,demonstrating that a better precision and high computational efficiency canbe achieved.

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